Combining Edge & Vertex Bevel
This is because the second bevel is trying to bevel edges which shouldn't be beveled, creating too much geometry, thus creating the artifacts.

You will see that if you set the limit method in the second bevel to "Angle" and then progressively increase the angle, at some point the artifacts will disappear.
Notice how the vertices count in the lower right corner drops while you increase the angle limit. Alternatively you can set the view to wireframe (SHIFT + Z) in order to see exactly which edges are beveled.

The angle refers to the angle between the two face connected by the edge, 180° being coplanar faces, 90° being faces at a right angle and 0° being faces that intersect each other (also coplanar).

No limit Vs Angle limit = 21° :